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If the ratio of sides between two similar figures is 6/11, then what would be the area and perimeter ratios?

Sagot :

jcherry99

Answer:

Step-by-step explanation:

Perimeter

Let the smaller figure have n sides

Then the perimeter of the smaller figure  = n * s

The perimeter of the larger figure = n*s1

The ratio would be n*s / n*s1 = 6/11 because the ns cancel out.

Area

The area is much harder.

If the figure is a regular polygon (all sides equal and convex) then both the sides and the apothem are both in a 6 to 11 ratio.

The formula for the area of a regular polygon is

Area = (n * s * a)/2

The apothem is the length of the line from the center of polygon to the middle of one of the sides.

S_L = the length of the larger side

S_s = the lenght of the smaller side

A_L = the length of the larger apothem

A_s = the length of the smaller apothem

Area_s = (n * S_L * A_L)/2

Area_L = (n * S_s * A_s)/2

The  2 s will cancel out

The ns will cancel out

S_s / S_L = 6/11

A_s / A_L = 6/11

Area_s / Area_L = (6 / ll ) ^2

Area_ s / Area_L = 36/121

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